the basic premise of "crit failures are more likely" is definitely trueIt's not. 11 is not the middle of a d20. 10.5 is.
If you do your math based on 11 being the middle, yeah, it'll seem like crit failures are more likely. And if you do your math based on 10 being the middle, it'll seem like crit successes are more likely.
You are right that 10.5 is the exact middle of a d20 roll. But this is exactly why a DC 11 flat check results in a 50/50 chance. Half of the d20 is greater than 10.5 (11-20), and half is less (1-10). Since meeting a DC constitutes a success, DC 10.5 and DC 11 are equivalent for the discrete cases of a d20 roll. DC 10 is not the same as DC 11, as this would result in 11/20 rolls passing and 9/20 failing. Its counterpart is a DC 12 check, which has 11/20 rolls failing and 9/20 passing.
At DC 15 (DC11+4) you get: 5 points of success (15-19), 9 points of failure (6-14), 1 point of crit success (20), and 5 points of crit failure (1-5).
At DC 6 (DC10-4) you get: 10 points of success (6-15), 4 points of failure (2-5), 5 points of crit success (16-20), 1 point of crit failure (1).The critical success and failure mirror each other here perfectly. However you are more likely to succeed then fail because of ties going to the roller.
This situation is accurate, but you're drawing a very different (and I believe incorrect) conclusion from it. You're claiming that rolls are mirrored when crit ranges are equal. DC 6 and 15 would then be mirrored, as they each produce 5 of one kind of crit and 1 of the other. Each scenario then has an extra success relative to the number of failures of its mirror (10 and 5 success vs 9 and 4 failures) because "ties go to the roller", and successes are therefore more likely than failures.
I would instead argue that what defines "mirrored rolls" is when the total number of good (combined success and crit success) and bad (failure and crit failure) results mirror one another. DC 6 and 15 are then no longer mirrors, as the former has 15 good results and 5 bad, while the latter had 6 good and 14 bad. DC 7 and 15 (which again, center on DC 11) are mirrored, with a 14/6 split either way. However, of those fourteen good results for a DC 7 check, only four are crit successes (17-20) while five of the fourteen failures for a DC15 check are (1-5). Since one extra of the failures is being "upgraded" to a crit relative to the mirrored number of successes, a crit failure is thus easier to achieve than a crit success.
In general, I think people are attaching way too much weight to the case of matching the exact DC. The idea that "tying the DC goes to the roller" is an artifact of how we define DCs, not a separate rule in itself. "DC 15" is just a shorthand way of saying "15 and above succeeds, 14 and below fails". We could produce the same situation by defining DC as a number that has to be beaten rather than just met and set to DC 14 instead. In this case "ties" would go against the roller, but we haven't really changed the underlying mechanics of the game, just how they're expressed.
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Because success is determined by an even sided die the average is never going to be a whole number. But DCs have to be while numbers, and obviously so does the DC +10 or -10 (or -11 if you support that).
There is no mathematical way therefore to have a DC that is both equally likely to succeed/fail and equally likely to be +10/-10 of the DC.
My mirroring above was equal crit success & failure chances.
For equal positive results to negative results the DC11 gives you 50/50. If you needed to exceed the DC instead of meet it then the 50/50 DC would be DC10. As I mentioned in a previous post DC10 & 11 mirror each other for crit chances. Because of the natural 1 & 20 rule in either of these set ups the 50/50 DC is perfectly even.
The centre for success/failure and the centre for crits cannot be the same. So they mirror each other differently.
The only time you are ever going to be dealing with 50/50 chances the crit success and failure is the same (natural 1 or 20). When it’s not a 50/50 roll it all comes down to the DC that had been set.
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The centre for success/failure and the centre for crits cannot be the same. So they mirror each other differently.
Well, right there you've hit upon the underlying issue of this thread: why shouldn't they be the same? That would seem like the most natural design choice. But for that to be accomplished, we need to have DC-10 still be a failure, and DC-11 be the first crit fail. Then, starting from the dividing line between success and failure, there are ten numbers in either direction before we hit either crit range. Having one side be ten numbers to crit and the other only nine just doesn't make as much sense.
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Well, right there you've hit upon the underlying issue of this thread: why shouldn't they be the same? That would seem like the most natural design choice. But for that to be accomplished, we need to have DC-10 still be a failure, and DC-11 be the first crit fail. Then, starting from the dividing line between success and failure, there are ten numbers in either direction before we hit either crit range. Having one side be ten numbers to crit and the other only nine just doesn't make as much sense.The centre for success/failure and the centre for crits cannot be the same. So they mirror each other differently.
Because the designers of PF2 do not want to introduce fractions into the game (cases like "half damage" are division rounded to whole numbers rather than fractions), the DC must be an integer. If we say, "Every result above the DC is a success and every result below the DC is a failure," then we have an undefined case in the middle, where a tie occurs.
On the other hand, the designers chose to use a format, "Every result that exceeds the DC by 10 or more is a critical success and every result that falls below the DC by 10 or more is a critical failure." That one is symmetrical and well defined, since the results between DC - 10 and DC + 10 ought to be covered by the normal success and normal failure rules. However, we have an odd number of results between DC - 10 and DC + 10, so normal failure and normal success cannot be balanced at equal numbers of results.
In comment #181 above, Liegence said,
I think of it more as 9 degrees of failure before crit failure, and 9 degrees of success before crit success BUT you also win ties. 9 + you win ties seems like it’s favorable, not unfavorable (really depends who’s rolling).
I like Liegence's explanation. Between DC - 10 and DC + 10 we have 9 clear results of success, 9 clear results of failure, and 1 tie. Since the designers wanted 4 degrees of success rather than 5 degrees of success, they defined the tie as a normal success. But that moves the dividing line between normal failure and normal success to a different point than the line of symmetry halfway between critical failure and critical success.
Anyone who demands perfect symmetry can invent a special rule for resolving ties, such as flipping a coin.
On the other hand, the designers chose to use a format, "Every result that exceeds the DC by 10 or more is a critical success and every result that falls below the DC by 10 or more is a critical failure."
Except they changed this language from the play test to the CRB. They did not say “falls below the DC by 10” they said “fails by 10 or more.” Which heavily implied to me that you would have to consider the first value that is a failure before counting.
This language shift occurs 2x in the CRB, but then is countered in the glossary, creating a fair bit of confusion. They could have left the language as you propose from the playtest that confirms directly with what is in the glossary, and the intended interpretation would have been clear.
Well, right there you've hit upon the underlying issue of this thread: why shouldn't they be the same? That would seem like the most natural design choice. But for that to be accomplished, we need to have DC-10 still be a failure, and DC-11 be the first crit fail. Then, starting from the dividing line between success and failure, there are ten numbers in either direction before we hit either crit range. Having one side be ten numbers to crit and the other only nine just doesn't make as much sense.The centre for success/failure and the centre for crits cannot be the same. So they mirror each other differently.
Probably comes down to ease of play. +10/-10 is easier to remember and probably sounds fair on paper. DC 15 and you crit on a 25 and crit fail on a 5 is easier to process on the fly. So I think it’s a more natural play experience.
The two chances odds being equal at the same point aren’t as important as ease of play for a couple of reasons. 1) +10 and -10 never come up on the same die roll. 2) the rule is consistent across the game including PCs, NPCs & Monsters so nobody is unfairly advantaged 3) the game doesn’t seem to balance itself around DC11 + or - any number.
An untrained simple DC is DC10. A 1st lvl DC is 15 which is somewhere between really hard if you are untrained with a bad attribute (-1 or 0 to the roll) or easy if you are trained with 18 in the stat (+7) to the roll. The book says these easier as you go up in level.
So with 9 numbers between crit fail and fail and 10 numbers between success and crit success are you more likely to crit fail more or crit succeed more? That depends entirely on the DC and your modifier.
Except they changed this language from the play test to the CRB. They did not say “falls below the DC by 10” they said “fails by 10 or more.” Which heavily implied to me that you would have to consider the first value that is a failure before counting.
As has been mentioned a lot. You can’t fail by 0, that’s just success.Your first failure is failing by 1. If they were going to make it DC -11 they would have kept the old language and changed the number.
On the other hand, the designers chose to use a format, "Every result that exceeds the DC by 10 or more is a critical success and every result that falls below the DC by 10 or more is a critical failure."Except they changed this language from the play test to the CRB. They did not say “falls below the DC by 10” they said “fails by 10 or more.” Which heavily implied to me that you would have to consider the first value that is a failure before counting.
This language shift occurs 2x in the CRB, but then is countered in the glossary, creating a fair bit of confusion. They could have left the language as you propose from the playtest that confirms directly with what is in the glossary, and the intended interpretation would have been clear.
I think you're over-thinking "language shift" by contrasting the CRB with the playtest.
Put yourself in the shoes of someone coming to the game fresh. They need to roll an 18 to succeed and instead roll an 8, the DM asks "Did you fail by 10 or more?"
What are they going to say?
"I failed by 10, so yes." seems like the only real reply, doesn't it?
If they then go to check the glossary they find it's entirely consistent with this interpretation.
I can see why you got to where you did, I just think it's because you're reading in a whole lot of text which isn't actually part of the rules and trying to reconcile that no-longer-relevant text is why it seems confusing to you.
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On the other hand, the designers chose to use a format, "Every result that exceeds the DC by 10 or more is a critical success and every result that falls below the DC by 10 or more is a critical failure."Except they changed this language from the play test to the CRB. They did not say “falls below the DC by 10” they said “fails by 10 or more.” Which heavily implied to me that you would have to consider the first value that is a failure before counting.
This language shift occurs 2x in the CRB, but then is countered in the glossary, creating a fair bit of confusion. They could have left the language as you propose from the playtest that confirms directly with what is in the glossary, and the intended interpretation would have been clear.
The "fails by X or more" language has been used for 10 years of Paizo products, plus 9 more years of D&D products before that (appearing in 2000 in the 3.0 Player's Handbook). A language shift from playtest to release, to be consistent with Paizo's other products, is in no way an indication that the math has changed since the playtest.
If we want to know how Paizo interpreted "fails by X or more" in PF1, we can look at this post from Sean Reynolds in 2011, where he describes a result of 5 on a DC 10 check as failing by 5 or more.
Now, is it possible that Paizo decided that a phrase that has been used in Pathfinder and its parent game for 19 years would mean something different in PF2? Sure. Is it remotely likely that they decided to make this change without telling anyone? No.
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And now for some numbers!
I made a spreadsheet to calculate every possible outcome for rolling a DC 20 check with modifiers ranging from +0 to +19. 20 rolls each with 20 potential outcomes - 400 combined outcomes. Here's the results:
64 critical fail (16%)
127 non-critical fail (31.75%)
144 non-critical success (36%)
65 critical success (16.25%)
So, this idea that if we interpret "fails by 10 or more" as "DC-10 or worse", we will make critical failures more likely than critical successes? I completely reject that.
If anyone would like to check the spreadsheet for errors or to make a copy to play with, here's a link. You can adjust the DC by changing cell A1. Red 1's are crit failures, yellow 2's are failures, etc.
(Note that the reason I used a DC 20 check with a scaling modifier, instead of a flat check with a scaling DC, was to prevent the rules regarding flat checks with DCs <= 1 and >= 21 from skewing the results)
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64 critical fail (16%)
127 non-critical fail (31.75%)
144 non-critical success (36%)
65 critical success (16.25%)So, this idea that if we interpret "fails by 10 or more" as "DC-10 or worse", we will make critical failures more likely than critical successes? I completely reject that.
That's an example where success is more likely than failure, yet critical success and critical failure are balanced.
If we change the DC to 21, we get:75 critical fail (18.75%)
134 non-critical fail (33.5%)
136 non-critical success (34%)
55 critical success (13.75%)
So in this case the non-criticals are pretty much balanced, but the criticals aren't.
(I'm OK with this. Critical failures for spell saves are more interesting than critical hits for attacks.)
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I get depressed seeing that this subject is pretty much the only topic discussed lately.
Then how about a discussion involving stealth, and initiative? Or how perception is covering everything from detecting lies to searching a room? Or how splash damage has no clear definition in the CRB?
So, what is your favorite rules topic? ;)
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And now for some numbers!
I made a spreadsheet to calculate every possible outcome for rolling a DC 20 check with modifiers ranging from +0 to +19. 20 rolls each with 20 potential outcomes - 400 combined outcomes. Here's the results:
64 critical fail (16%)
127 non-critical fail (31.75%)
144 non-critical success (36%)
65 critical success (16.25%)So, this idea that if we interpret "fails by 10 or more" as "DC-10 or worse", we will make critical failures more likely than critical successes? I completely reject that.
If anyone would like to check the spreadsheet for errors or to make a copy to play with, here's a link. You can adjust the DC by changing cell A1. Red 1's are crit failures, yellow 2's are failures, etc.
(Note that the reason I used a DC 20 check with a scaling modifier, instead of a flat check with a scaling DC, was to prevent the rules regarding flat checks with DCs <= 1 and >= 21 from skewing the results)
Alright, first of all: that's actually a nice tool! Thanks for putting that together. I might hang on to a copy of that in the future if you don't mind...
However, we need some edits for this particular application. As it stands now, you're using a biased selection pool. If we were to use only the bottom half of your table we would erroneously conclude that it was nearly impossible to crit fail, but that's clearly not the case. Notice how in the bottom row it's impossible to crit fail? You need one more at the top where it's impossible to crit succeed.
To accomplish this, I've made a version where I've added an extra row with a +20 modifier and upped the DC to 21 to compensate. Now, ignoring crits, this scenario runs the full range from impossible to reach the DC (20+0) to impossible to miss (1+20). If we total up results now, we have 210 each of general successes and failures, but ten more crit failures than failures!
I've also made a second sheet in the same workbook that repeats the calculations but using DC-11 and below as crit fails. In this case, we again have 210 each of general successes and failures, but the crits are also equal at 65 apiece. This is what I mean when I say that crit fails are more likely under the current rules.
I'll concede that it would take a little more effort in play to remember, and since this rule applies to all parties it's "balanced" in the sense that it hurts everyone equally. It isn't something that necessarily needs to be changed (though I'll certainly be house ruling it). But it is a mathematical fact that these rules favor crit fails over crit successes on an even distribution over various DCs.
Essentially, the problem is this:
Hey! You've show Paizo an opportunity for a 5th result... when the roll exactly matches the DC.
Crit Success = +10 and beyond
Success = +1 to +9
New Result = +0
Failure = -1 to -9
Crit Failre = -10 and beyond
Barely hit? Shields soak 2x hardness? :)
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Franz Lunzer asked the a very simple and unbiased question to help resolve this on the thread post for questions for pathfinder Friday. Rather than attempt to answer it, and move this discussion there, I suggest folks like the question a whole lot so it is clear that this is a question that we would like answered by a developer.
You can see it here.
From the other thread:
For a recovery check at Dying 2 (DC12), is a natural 2 result a failure or a critical failure?
I just re-watched the 3-action game night game on YouTube, and Jason Bulmahn more or less directly answered this question by stating (regarding a recovery save)
it is going to be a flat check, the DC is 12, which means, on a 1 or a 2 you die
So, RAW and RAI seem to match. Time to house-rule.
Interesting assumption. I don't assume that anyone outside of this thread ever considered an issue to exist.
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One side argues that just like "success by zero" means rolling exactly 32, "failure by zero" must then mean rolling 31.
I get the impression that there are about five people in the world who think this, and everyone else thinks the other thing.
Where can we find the RAW answer?
Just above.
It is going to be a flat check, the DC is 12, which means, on a 1 or a 2 you die
Needing a 12 and rolling a 2 is a failure by 10.
So DC 32 looks like this:
42 is just good enough to be a critical success
32 is just good enough to be a success
22 is just bad enough to be a critical failure
So DC 32 looks like this:
42 is just good enough to be a critical success
32 is just good enough to be a success
22 is just bad enough to be a critical failure
I like this more elegant and mathematically better interpretation:
So DC 32 looks like this:42 is just good enough to be a critical success
32 is just good enough to be a success
22 is just good enough to be a failure
Keeps the steps at 10 difference, using the same language everywhere. It was already mentioned earlier, one page back.
I like this more elegant and mathematically better interpretation:
So DC 32 looks like this:
42 is just good enough to be a critical success
32 is just good enough to be a success
22 is just good enough to be a failure
You're entitled to whatever house rule you like, but the intended rule:
DC+10 is a critical successDC-10 is a critical failure
is elegant enough for most people.
...why did we need to necro a 14-month-old thread?
Because the ongoing lack of official developer clarifications of rules like this, Battle Medicine, Mountain Stance, Battle Forms, etc. is leaving people dissatisfied.
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As long as we have rules written in words instead of machine code, everything can be interpreted in a myriad of different ways.
This case is not worth a clarificaton, IMO.
As a firm believer that having the categories of success and failure each have 10 numbers within them would have been the much more elegant and intuitive system, and that the language in the Core rulebook could be interpreted to favor it, the glossary entry is counter to that interpretation and it seems, from live streams, that the developers interpret 10 less than the DC as a critical failure, so it seems like RAI is unfortunately counter to mathematical symmetry.
It would still be nice if more developers could do things like Mark and Linda have done with the Arcane Mark twitch stream where they don't say what the rules are supposed to say but they do say how they have handled specific situations and often times why.
Jason Bulmahn has a youtube channel where he has run a bunch of arena fights with Dan(other paizo guy).
I am sure there are plenty of times there have been crit fails throughout the videos, I am pretty sure he goes with 10 less than the DC as opposed to fail by 10 when he runs those.
While, of course, nothing he does on his youtube channel is official, it is good enough for me to see how the guy who made the rules runs his games, and go with that ruling when unclear rules arise.
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Yes, mathematical symmetry is already broken by the fact that matching the DC exactly is a success. And for good reason, because I can't think of a way of resolving ties that doesn't complicate the game or involve useless rerolls.
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Yes, mathematical symmetry is already broken by the fact that matching the DC exactly is a success. And for good reason, because I can't think of a way of resolving ties that doesn't complicate the game or involve useless rerolls.
Agreed. Put another way, there's a succeed by zero: you meet the DC. So for this let's say DC 15. Get that fifteen? Succeed by zero.
How do you FAIL by zero?
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Agreed. Put another way, there's a succeed by zero: you meet the DC. So for this let's say DC 15. Get that fifteen? Succeed by zero.
How do you FAIL by zero?
In my opinion you don't, and if you don't things are clear.
DC20, roll 10, failed your target number by 10
.
DC20, roll 19, failed your target number by 1
DC20, roll 20, hit your target number (0)
DC20, roll 21, beat your target number by 1
.
DC20, roll 30, beat your target number by 10
Thats 21 numbers in total, however it very much fits the succeed by 10 and fail by 10 rules.
If you add a second zero result (failure by 0 or just failure) you now have 22 numbers and the crit fail result for the above example would only start at a roll of 9 instead of 10. The later may be more symetrical, however also less natural, at least for my taste.
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Yes, mathematical symmetry is already broken by the fact that matching the DC exactly is a success. And for good reason, because I can't think of a way of resolving ties that doesn't complicate the game or involve useless rerolls.How isn't easy to imagine
DC 42 Critical success
DC 32 Success
DC 22 Failure
Critical Failure...?
That's not what they said. They are talking about:
43+ Critical Success
33-42 Success
32 ....?
22-31 Failure
21- Critical failure
as a means to have ten results above the DC granting success and 10 results below it resulting in failure while keeping everything to integers, for mathematical symmetry. Which of course is absurd... and also the point they were making.
That's not what they said. They are talking about:43+ Critical Success
33-42 Success
32 ....?
22-31 Failure
21- Critical failureas a means to have ten results above the DC granting success and 10 results below it resulting in failure while keeping everything to integers, for mathematical symmetry. Which of course is absurd... and also the point they were making.
I don't understand why you'd want to make it that complicated.
Either you have easy increments of DCs, such as
DC 42 Critical success
DC 32 Success
DC 22 Failure
...or your game has failed to keep things simple for no good reason. That's the point that SHOULD be made.
Zapp,
I 100% agree that this is what should have happened, but it really doesn't seem to be what did happen. A lot of people have managed to make up ways for them to remember why it doesn't work this way though, and the only real consequence of it I tend to see is that death and dying are more likely and more scary.
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I 100% agree that this is what should have happened, but it really doesn't seem to be what did happen.
I think that almost everybody who plays this game (including the developers) are pretty clear about what the rules say AND mean.
DC + 10 = critical successDC = success
DC - 10 = crit fail
There seem to be a tiny minority of people in this thread who think there is an issue.
There really isn't.
Its simple. Its perhaps a little inelegant and not quite symmetrical but its very clear that it is what it is.
And, as somebody who regularly sees players having difficulty adding 7 and 2 and 1, I'm firmly of the opinion that it was the right choice.
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For the people arguing about the lack of symmetry of +10 vs. -9;
There's a different symmetry here. If the DC is 25, then 35+ and 15- are crits. A difference of 1 on the most significant digit. Since our numeric system is base 10, it makes it really really easy to see whether a given result is a crit compared to the DC.
So it is symmetrical in the aspect that's most important: usability!
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I think it is fair to point out that the language in the core rule book is more ambiguous than it needs to be and would benefit from a little more clarity in the next reprint. It is an easy fix, as has been much discussed in this thread. Especially as large scale resolution came from the fact that all of the developers seem to play it one specific way on their live streams.
I don't see a fairness issue.
Win by 1-9? Success.
Lose by 1-9? Failure.
Win by 10+? Critical success.
Lose by 10+? Critical failure.
Tie? Defined as a success by the system. That's the crux of the whole situation and why it looks awkward.
Technically, there are more non-negative integers than negative. And no, we're not eliminating zeroes, it took the West long enough to accept the things we're not going to chuck them now.